Three points A, B and C lie in this order on a line, and P is any
point in the plane. Use the Cosine Rule to prove the following
statement.

Round and Round a Circle

Age 14 to 16 Challenge Level:

What do the numbers refer to?
Are they the same value more than once during the dot's motion
around the circle?
Are the three values connected and if so how?
Why not draw some graphs of the values to help explain what you
find.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.